Academic journal article AEI Paper & Studies

Portfolio Diversification in Concentrated Bond and Loan Portfolios

Academic journal article AEI Paper & Studies

Portfolio Diversification in Concentrated Bond and Loan Portfolios

Article excerpt

ABSTRACT

I develop an algorithm to approximate the loss rate distribution for fixed income portfolios with obligor concentrations. The approximation requires no advanced mathematics or statistics, only the summation of large exposures and the evaluation of binomial probabilities. The approximation is model-independent and can be used after removing default dependence using any risk modeling approach. It is especially useful for capital calculations given its inherent accuracy in the upper tail of the cumulative portfolio loss rate distribution. The approximation provides a simple way to calculate the capital needed when a marginal credit is added to a concentrated portfolio.

Key Words: Portfolio diversification, idiosyncratic default risk, obligor concentration, Vasicek single common factor model of credit risk, credit value at risk, Basel bank capital requirements

I. Introduction

Compound interest and risk diversification, if not among the most powerful forces in nature, are still perhaps the two most important forces in finance. (2) The modern theory of portfolio diversification began when Markowitz (1952) emphasized the importance of efficient mean-variance portfolios for investment management. Markowitz's insights lead to the development of Sharpe's (1964) Capital Asset Pricing Model, the first equilibrium model that links risk and expected return.

Despite the fundamental importance of diversification, it took almost 50 years after Markowitz's original insights before formal diversification techniques were adopted to manage high-quality loan and bond portfolios. For example, according to Altman and Saunders (1998), " [While] one might expect that these very same [Markowitz] techniques would (and could) be applied to the fixed income area ...there has been, however, very little published work in the bond area and a recent survey of practices by commercial banks found fragmented and untested efforts." (p. 1728)

There are many reasons why fixed income managers were slow to adopt formal portfolio diversification models. One is that it is not so obvious how diversification works for fixed income investments given the abbreviated nature of their positive return tails. Moreover, fixed income investments often are not actively traded and most lack the return histories necessary to construct Markowitz efficient portfolios. Finally, fixed income investments tend to be discrete, meaning that they come in prepackaged sizes that may be large and not as easily disaggregated and traded. This discrete, illiquid nature makes it inherently difficult and expensive to diversify a portfolio of fixed income claims and consequently many credit portfolios contain obligor concentrations--large unbalanced exposures to a borrower or multiple borrowers. Obligor concentrations can significantly reduce portfolio diversification.

In this paper, I develop a simple algorithm to approximate the loss rate distribution of a fixed income portfolio with obligor credit concentrations. The intuition that underlies the approximation is easy to understand and the approximation calculations require no advanced mathematics or statistics--only the summation of a portfolio's largest loss exposures and an evaluation of binomial probabilities. Unlike the so-called "granularity adjustment" approach for measuring concentration risk, this approximation is not model-dependent. (3) It can be used after removing obligor default dependence using any risk modeling approach. The approximation is especially useful for capital calculations as it is very accurate for the upper tails of the cumulative portfolio loss rate distribution. The approximation also provides a simple and intuitive method for calculating the "value-at-risk" capital increment that is required when a new obligor is added to a concentrated credit portfolio.

The paper is organized as follows. Section II provides an abbreviated overview of the development of formal portfolio diversification models for high-quality fixed income portfolios including the granularity adjustment approach for measuring obligor concentration risk. …

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